I am a right-handed quilter only. I use a ThimbleLady thimble on my middle finger. These are cone-shaped; open-ended thimbles with very deep dimples. I also use Roxanne needles - usually #11's but sometimes #12's. Try loading only 2-3 stitches onto your needle. What I do is have my left hand - pick a finger - positioned underneath where the needle will be coming through the sandwich. Pretty much just as it lightly pricks your bottom finger, I sort of use the thumb of my right hand to help with the 'rocking' part of bringing the needle back up to the top of the sandwich by placing it on the top of the sandwich to kind of make the sandwich a bit stiffer for that few seconds. Not sure that easily translated into words but hopefully it made sense. I also use a rubber finger tip on my index finger of my right hand to help pull the needle through. Sometimes if I load a lot of stitches on the needle I might even need a pair of pliers to help pull the needle through.
One reason I like the ThimbleLady thimbles is that you are pushing with the pad of your finger vs the tip. I find it much more comfortable for longer quilting sessions.